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The Unity of Science in Early-Modern Philosophy: Subalternation, Metaphysics and the Geometrical Manner in Scholasticism, Galileo and Descartes

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The Unity of Science in Early-Modern Philosophy: Subalternation, Metaphysics and the Geometrical Manner in Scholasticism, Galileo and Descartes by Zvi Biener M.A. in Philosophy, University of Pittsburgh, 2004 B.A. in Physics, Rutgers University, 1995 B.A. in Philosophy, Rutgers University, 1995 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 2008 UNIVERSITY OF PITTSBURGH FACULTY OF ARTS AND SCIENCES This dissertation was presented by Zvi Biener It was defended on April 3, 2008 and approved by Peter Machamer J.E. McGuire Daniel Garber James G. Lennox Paolo Palmieri Dissertation Advisors: Peter Machamer, J.E. McGuire ii Copyright c by Zvi Biener 2008 iii The Unity of Science in Early-Modern Philosophy: Subalternation, Metaphysics and the Geometrical Manner in Scholasticism, Galileo and Descartes Zvi Biener, PhD University of Pittsburgh, 2008 The project of constructing a complete system of knowledge—a system capable of integrating all that is and could possibly be known—was common to many early-modern philosophers and was championed with particular alacrity by Ren´eDescartes. The inspiration for this project often came from mathematics in general and from geometry in particular: Just as propositions were ordered in a geometrical demonstration, the argument went, so should propositions be ordered in an overall system of knowledge. Science, it was thought, had to proceed more geometrico. I offer a new interpretation of ‘science more geometrico’ based on an analysis of the explanatory forms used in certain branches of geometry. These branches were optics, as- tronomy, and mechanics; the so-called subalternate, subordinate, or mixed-mathematical sciences. In Part I, I investigate the nature of the mixed-mathematical sciences accord- ing to Aristotle and some ‘liberal Jesuit’ scholastic-Aristotelians. In Part II, I analyze the metaphysics and physics of Descartes’ Principles of Philosophy (1644, 1647) in light of the findings of Part I and an example from Galileo. I conclude by arguing that we must broaden our understanding of the early-modern conception of ‘science more geometrico’ to include concepts taken from the mixed-mathematical sciences. These render the geometrical manner more flexible than previously thought. iv TABLE OF CONTENTS PREFACE ......................................... ix 1.0 INTRODUCTION ................................. 1 1.1 THE UNITY OF SCIENCE IN EARLY-MODERNITY ........... 3 1.2 THE CENTRAL ARGUMENT: THE UNITY OF SCIENCE, THE GEO- METRICAL MANNER AND SUBALTERNATION ............. 7 1.3 THE BIRTH OF MATHEMATICAL PHYSICS ................ 9 1.4 PRELIMINARY I: DELIMITING TRADITIONS ............... 11 1.5 PRELIMINARY II: DEFENDING MIXED-MATHEMATICS AS A SUB- JECT OF STUDY ................................ 15 1.6 PLAN OF THE WORK ............................. 17 2.0 THE TEMPERED-HYLOMORPHISM OF MIXED-MATHEMATICS 20 2.1 MIXED-MATHEMATICS: THE BASIC FRAMEWORK ........... 21 2.1.1 THE DEDUCTIVE STRUCTURE OF ARISTOTELIAN SCIENCE . 22 2.1.2 THE GENERIC STRUCTURE OF PHYSICAL AND MATHEMATI- CAL OBJECTS .............................. 24 2.1.3 GENERA CROSSING: THE MIXED-MATHEMATICIAN’S MODE OF THOUGHT .............................. 27 2.2 TEMPERED-HYLOMORPHISM: A CASE STUDY OF PHYSICS II.2 .. 30 2.2.1 THE ARGUMENTATIVE STRUCTURE OF PHYSICS II.1–2 .... 31 2.2.2 THE PLATONIST AND THE CONTRAPUNTAL STRUCTURE OF PHYSICS II.2 ............................... 34 2.2.3 THE SUBORDINATE SCIENCES: A SEPARATE QUESTION? ... 38 v 2.2.4 The Disciplinary Integrity and Nature of the Subordinate Sciences .. 40 2.2.5 A QUALIFIED RECOMMENDATION ................. 42 2.3 CONCLUSION (AND A LITTLE MORE) ................... 44 3.0 SUBALTERNATION, METAPHYSICS AND THE UNITY OF SCI- ENCE ......................................... 46 3.1 SETTING THE SCENE ............................. 47 3.2 UNITY, SUBALTERNATION, AND METAPHYSICS IN EUSTACHIUS . 51 3.3 IMPLICATIONS AND CONCLUSIONS .................... 61 3.4 FURTHER EVIDENCE: SUBALTERNATION AND METAPHYSICS IN SUAREZ´ ..................................... 63 4.0 TEMPERED-HYLOMORPHISM AND GALILEO’S SCIENCE OF MAT- TER .......................................... 69 4.1 INTRODUCTION ................................ 69 4.2 THE NATURE OF MATTER AND THE NEW SCIENCE ......... 72 4.3 THE MATHEMATICAL FOUNDATIONS OF THE NEW SCIENCE .... 77 4.4 THE APPLICATION OF MATHEMATICS JUSTIFIED ........... 84 4.5 TEMPERED-HYLOMORPHISM AND SUBALTERNATION ........ 86 5.0 THE SUBALTERNATION OF PHYSICS TO METAPHYSICS IN DESCARTES 94 5.1 INTRODUCTION: A DEMARCATION PROBLEM? ............ 94 5.2 THE ASSUMPTIONS BEHIND THE DEMARCATION PROBLEM .... 98 5.3 PHYSICS AND METAPHYSICS IN THE PRINCIPLES .......... 109 5.4 BODY AND MOTION ............................. 113 5.4.1 THE ARGUMENT FROM ELIMINATION ............... 115 5.4.2 THE COMPLETE CONCEPT ARGUMENT (AND THE CONCEPT OF SUBSTANCE) ............................. 118 5.4.3 MOTION .................................. 125 5.5 SUBALTERNATION IN ACTION: THE DEDUCTION OF THE LAWS OF NATURE ..................................... 130 5.6 CONCLUSION AND CIRCUMSTANTIAL EVIDENCE ........... 136 vi 6.0 CONCLUSION: THE UNITY OF SCIENCE AND THE GEOMETRI- CAL MANNER .................................. 140 APPENDIX A. EUSTACHIUS A SANCTO PAOLO: SUMMA PHILOSOPHIAE 143 APPENDIX B. FRANCISCO SUAREZ:´ DISPUTATIONES METAPHYS- ICAE ......................................... 148 BIBLIOGRAPHY .................................... 152 vii LIST OF FIGURES 1 Discorsi, Second Day: Longitudinal Pull Case .................. 79 2 Discorsi, Second Day: Cantilever Case ...................... 92 3 Discorsi, Second Day: Balance Case I ...................... 92 4 Discorsi, Second Day: Balance Case II ...................... 93 5 Discorsi, Second Day: Galileo’s Proof of the Law of the Lever ......... 93 6 Principles: The Composition of Motions ..................... 130 viii PREFACE Much too often, this dissertation came close to never being written. The fact that it is now written is due to the presence and patience of several people. First are my advisers, Ted McGuire and Peter Machamer. Ted McGuire’s guidance in the early years of my education is responsible for the arc of my academic trajectory. He first introduced me to history as a way of practicing philosophy and to the seventeenth- century as particularly rich field of study. Moreover, throughout my years in Pittsburgh, Ted has repeatedly exemplified for me the true scholarly stance. His passion and kind-hearted criticism always energize and are matchless in our Hobbesian academic world. Many years will pass before I can inspire so effortlessly. Peter Machamer has easily been the greatest influence on this dissertation. Without his advice, I would have never fixed on the subalternate sciences as a subject of study and without his insight, I would have never seen clear through the problems they pose. Peter’s kind words are few but unquestionably genuine, and his kind actions are equally genuine yet innumerable. For all of them, I am grateful. Peter’s example will also be lasting: in our academic world of res cogitantes, Peter philosophizes as a doer. Many years will pass before I can get to the heart of things half as fast. Jim Lennox and Paolo Palmieri have been invaluable committee members. In the great loneliness of authorship, I heard their uncompromisingly sharp criticisms echoing around me more than those of any others. Perhaps without them I would have paused less while writing, but my writing would have undoubtedly suffered. Paolo deserves additional thanks for structuring some of his courses to my needs and tolerating my juvenile Latin. Jim deserves additional thanks for talking at length about Chapter 2 and sharing with me his own paper on the same subject. ix Dan Garber’s support and willingness to work with me despite a paucity of drafts has been truly unbelievable. I wish I had been more productive and more punctual, so that I could have worked with him more. As things stand, I can only thank him profusely. Apart from our actual interactions, it was Dan’s work on Mersenne and Galileo that convinced me that the subject of mixed-mathematics in the early seventeenth-century is worth investigat- ing, and I’d like to thank him, once again, for that. Fellow brunchers Erik Anger, Brian Hepburn, and David Miller read very early drafts of these ideas and helped me get started with writing. Chris Smeenk, although not involved with this dissertation, has been a steady cheerful presence in my intellectual life. To all, thank you. And finally, my eternal and unending gratitude goes to Kate, who smiles at my flights of fancy and bears me when I’m down. She is my true companion. I would have given up without her, a long time ago. x ABBREVIATIONS Unless otherwise noted, the following translations and editions of primary sources are used. Physics Charlton, William (1970). Aristotle’s Physics. Books I & II. Oxford: Claren- don Press. Summa Eustachius a Sancto Paulo (1609). Summa philosophiae quadripartita, de rebus Dialecticis, Ethicis, Physicis, & Metaphysicis. Paris. Disputationes Su´arez, Francisco (1597). Disputationes Metaphysicae. Salamanca. Edi- tion of 1619 reproduced in Opera Omnia (vol. 25–26), Hildesheim: Olms, Metaphysicae 1965. Text reproduced by Salvador Castellote, Jean-Paul Coujou and John P. Doyle at http://homepage.ruhr-uni-bochum.de/Michael.Renemann/ suarez/index.html Principles Descartes, Ren´e (1983 [1644]). Principles of Philosophy, trans. V. R.
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